Yet another scarf pattern - the theory

It has been observed that popular movies inspire any number of trends. Those who participate in these trends may do so because they seek to emulate the characters or actors in the movie, or perhaps to demonstrate allegiance to an ideal exemplified in the movie. Regardless of the motivation, it appears that an alarming number of red-and-yellow striped scarves have been produced as a result of a certain movie released in 2001 based on a popular children’s book (there is, in fact, a debate regarding the correct colours of the scarf-red or burgundy? Yellow or old gold?). Many of these scarves were mass-produced on a commercial scale; others were made by hand, usually for non-commercial purposes. Consequently, there has been a demand for a (free) pattern for this striped scarf, which is available from other sources.

Some might consider it surprising that knitters, who are capable of knitting in stockinette and stripes without explicit pattern directions, must rely on written instructions to make what is, in effect, a long scarf knit in stockinette and stripes. Perhaps there is some degree of uncertainty in the dimensions of the “real” scarf used in the movie; however, as a comparison of illustrations and movie stills reveals, without direct knowledge of the scarves produced as part of the characters’ costumes, it is extremely difficult to determine the true length, width, or stripe proportions of the scarf. Therefore, let us consider a theoretical scarf, and the equations by which a formula for knitting this scarf may be derived.

The scarf comprises an odd number of stripes, as can be discerned from illustrations and the movie, based on the alternating colour pattern and the fact that the scarf begins and terminates with the same colour. The total number of stripes may be defined as

where n is an integer. This expression arises as the sum of n stripes of a first colour, and n + 1 stripes of the second colour.

Further observation of the scarf suggests that the width of the scarf, in relation to the length of a single stripe, may be anywhere between 4:3 and 3:2. However, depending on the illustration or picture used to make such a determination, the ratio of width to length varies. If we take w as the width of the scarf and s as the length of a single stripe, as shown (l is the total length of the scarf, excluding fringe):

we may conclude that

Equation 1.

where r is the ratio of w to s (observation indicates that it is likely between 1.33 and 1.5). Furthermore,

Equation 2.

We now have two equations and three variables which must be given values in order to compute the characteristics of the scarf (only one of the variables w and s is required, as there is a scalar relationship between the two). However, before we proceed, it should be noted that:

The scarf, as observed, appears to be doubled, as in a knitted tube; and

The scarf, as observed, has approximately fifteen stripes, beginning and ending with red.

This latter point is inferred from an observation of the scarf draped around Ron Weasley’s neck; it appears that the eighth stripe thereof is located at the back of the neck.

Therefore, n is estimated at 7, and the second equation reduces to

Equation 3.

And consequently

Equation 4.

Thus, if a value is assigned to l (in practical application, this could be ascertained by draping a measuring tape around the recipient’s neck) and to r, values for w and s may be calculated according to Equations 4 and 1.

Let us consider the value of r. If we arbitrarily assign a scarf length of 72", then an r value of 1.33 results in a total scarf width of 6.4"; this is sufficiently wide, but some observations of the movie scarf suggest that the width may be greater in proportion to the length. If we use r = 1.5, then w = 7.2". This is likely a more comfortable and useful width for a scarf. r, however, may be adjusted according to the user’s aesthetic preferences.

Having l and r, and consequently w and s in hand, it is now time to consider the actual knitting instructions. It is first necessary to consider the first note above, namely that the scarf appears to be doubled in width. Therefore, in creating the pattern instructions, one should use the value 2w for the scarf width. This is incorporated below. It is necessary to assign two new variables:

is the unitary stitch gauge of the yarn; and

is the unitary row gauge of the yarn.

The units should be consistent throughout all calculations; for example, using inches as the unit of measurement, the length l and width w would be determined in inches, and g_s and g_r would be determined in stitches and rows per inch.

To commence the scarf, the first colour (red) should be cast on for a total of

These stitches should be joined, if it is desired to work in the round, or not, if the user intends to seam the scarf afterwards.

Red is then worked in stockinette for a total of

The colour is then broken, and yellow joined, and worked in stockinette for a total of

These alternating s g_r rows of colour are worked until there are n (seven) yellow stripes, and n + 1 red stripes. The scarf should then be l long. The knitting is then bound off and the ends (and long edges, if necessary) seamed, for a resultant width w.

Odd numbers of tassels are then applied to the ends of the scarf, commencing with red and alternating with yellow. Observation suggests that a minimum of five tassels be used; there may be as many as nine or eleven at each end. The total length of the tassels, trimmed, should be approximately s.

This particular implementation places the scarf width w in dependency on the desired length l, and number and proportions of each stripe. This can result in an undesirably narrow width w. A more practical application allows the user to fix an approximate l and w based on empirical knowledge, and allow the stripe proportion factor ror the number of stripes n to fall where they may. In this manner, a scarf of useful dimensions is generated, with similar characteristics to the idealized product. The pattern generation procedure used herein follows this practice.

The Quidditch Sweater is left as an exercise to the reader.